{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Seeded Graph Matching (SGM)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import random\n",
    "np.random.seed(8888)\n",
    "rng = np.random.default_rng(8888)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Seeded Graph Matching (SGM) is a version of the graph matching problem where one is first given a partial alignment of the nodes. This algorithm is an modification of the Fast Approximate QAP (FAQ) algorithm (Vogelstein, 2015), as described in Seeded graph matching (Fishkind, 2018). For a more in depth explanation of the graph matching problem and FAQ, view the FAQ tutorial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "from graspologic.match import graph_match\n",
    "from graspologic.plot import heatmap\n",
    "from graspologic.simulations import er_corr, sbm, sbm_corr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SGM on Correlated Graph Pairs\n",
    "To demonstrate the effectiveness of SGM, the algorithm will be applied on a pair of correlated SBM graphs (undirected, no self loops) $G_1, G_2 \\sim SBM\\,(n, p, rho)$  with the following parameters:\n",
    "\\begin{align*}\n",
    "n &= [100, 100, 100]\\\\\n",
    "p &= \\begin{bmatrix} \n",
    "0.7 & 0.3 & 0.4\\\\\n",
    "0.3 & 0.7 & 0.3\\\\\n",
    "0.4 & 0.3 & 0.7\n",
    "\\end{bmatrix}\\\\\n",
    "rho &= 0.9\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x360 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "directed = False\n",
    "loops = False\n",
    "n_per_block = 75\n",
    "n_blocks = 3\n",
    "block_members = np.array(n_blocks * [n_per_block])\n",
    "n_verts = block_members.sum()\n",
    "rho = .9\n",
    "block_probs = np.array([[0.7, 0.3, 0.4], [0.3, 0.7, 0.3], [0.4, 0.3, 0.7]])\n",
    "fig, ax = plt.subplots(1, 1, figsize=(4, 4))\n",
    "sns.heatmap(block_probs, cbar=False, annot=True, square=True, cmap=\"Reds\", ax=ax)\n",
    "ax.set_title(\"SBM block probabilities\")\n",
    "\n",
    "A1, A2 = sbm_corr(block_members, block_probs, rho, directed=directed, loops=loops)\n",
    "fig, axs = plt.subplots(1, 3, figsize=(10, 5))\n",
    "heatmap(A1, ax=axs[0], cbar=False, title=\"Graph 1\")\n",
    "heatmap(A2, ax=axs[1], cbar=False, title=\"Graph 2\")\n",
    "_ = heatmap(A1 - A2, ax=axs[2], cbar=False, title=\"Diff (G1 - G2)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To demonstrate the effectiveness of SGM, as well as why having seeds is important, we will randomly shuffle the vertices of Graph 2. This random permutation is stored, and unshuffled, such that we have available the optimal permutation that returns the original graph 2. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Shuffling graph 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we see that after shuffling graph 2, there are many more edge disagreements, as expected."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x360 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "node_shuffle_input = np.random.permutation(n_verts)\n",
    "A2_shuffle = A2[node_shuffle_input][:, node_shuffle_input]\n",
    "node_unshuffle_input = np.argsort(node_shuffle_input)\n",
    "\n",
    "fig, axs = plt.subplots(1, 3, figsize=(10, 5))\n",
    "heatmap(A1, ax=axs[0], cbar=False, title=\"Graph 1\")\n",
    "heatmap(A2_shuffle, ax=axs[1], cbar=False, title=\"Graph 2 shuffled\")\n",
    "_ = heatmap(A1 - A2_shuffle, ax=axs[2], cbar=False, title=\"Diff (G1 - G2 shuffled)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unshuffling graph 2 without seeds\n",
    "First, we will run SGM on graph 1 and the shuffled graph 2 with no seeds, and return the match ratio, that is the fraction of vertices that have been correctly matched."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Match Ratio with no seeds:  0.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x360 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_, perm_inds, _, _ = graph_match(A1, A2_shuffle, rng=rng)\n",
    "A2_unshuffle = A2_shuffle[perm_inds][:, perm_inds]\n",
    "\n",
    "fig, axs = plt.subplots(1, 3, figsize=(10, 5))\n",
    "heatmap(A1, ax=axs[0], cbar=False, title=\"Graph 1\")\n",
    "heatmap(A2_unshuffle, ax=axs[1], cbar=False, title=\"Graph 2 unshuffled\")\n",
    "heatmap(A1 - A2_unshuffle, ax=axs[2], cbar=False, title=\"Diff (G1 - G2 unshuffled)\")\n",
    "\n",
    "match_ratio = (perm_inds == node_unshuffle_input).mean()\n",
    "print(\"Match Ratio with no seeds: \", match_ratio)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While the predicted permutation for graph 2 did recover the basic structure of the stochastic block model (i.e. graph 1 and graph 2 look qualitatively similar), we see that the number of edge disagreements between them is still quite high, and the match ratio quite low. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unshuffling graph 2 with 10 seeds\n",
    "Next, we will run SGM with 10 seeds randomly selected from the optimal permutation vector found ealier. Although 10 seeds is only about 4% of the 300 node graph, we will observe below how much more accurate the matching will be compared to having no seeds."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Match Ratio with 10 seeds:  1.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x360 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "seeds1 = np.sort(random.sample(list(range(n_verts)),10))\n",
    "seeds1 = seeds1.astype(int)\n",
    "seeds2 = np.array(node_unshuffle_input[seeds1])\n",
    "partial_match = np.column_stack((seeds1, seeds2))\n",
    "    \n",
    "_, perm_inds, _, _ = graph_match(A1, A2_shuffle, partial_match=partial_match, rng=rng)\n",
    "A2_unshuffle = A2_shuffle[perm_inds][:, perm_inds]\n",
    "\n",
    "fig, axs = plt.subplots(1, 3, figsize=(10, 5))\n",
    "heatmap(A1, ax=axs[0], cbar=False, title=\"Graph 1\")\n",
    "heatmap(A2_unshuffle, ax=axs[1], cbar=False, title=\"Graph 2 unshuffled\")\n",
    "heatmap(A1 - A2_unshuffle, ax=axs[2], cbar=False, title=\"Diff (G1 - G2 unshuffled)\")\n",
    "\n",
    "match_ratio = (perm_inds == node_unshuffle_input).mean()\n",
    "print(\"Match Ratio with 10 seeds: \", match_ratio)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the results above, we see that when running SGM on the same two graphs, with no seeds there is match ratio is quite low. However including 10 seeds increases the match ratio to 100% (meaning that the shuffled graph 2 was completely correctly unshuffled)."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.9.7 ('.venv': poetry)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  },
  "vscode": {
   "interpreter": {
    "hash": "bc13b1df6b0248aaf34f3e7f5790740f6f355623370613abc0a11b70d06c20f2"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
